Suspension dynamics in transitional pipe flow

Abstract

Particle-laden pipe flows exhibit a gradual laminar-turbulent transition, beyond a critical volume fraction (φ). While classical transition behavior is characterized by the presence of turbulent puffs, this intermittent nature is absent for particle-induced transition. For small pipe-to-particle diameter ratios (D/d) even dilute systems exhibit this particleinduced transition behavior. In this study we use neutrally buoyant particles with a D/d of 5.7, which represents a "sweet spot," allowing the use of particle image velocimetry to study this particular phenomenon. The average velocity profile gradually changes from a parabola (laminar flow) to a blunted velocity profile for increasing Reynolds number. The instantaneous velocity profiles fluctuate around this profile. These velocity fluctuations, described by u x −rms and u r −rms, gradually increase for increasing Reynolds number, as do the Reynolds stresses. For low Re s , the velocity fluctuations increase proportional to the bulk velocity, which can be explained by a simple model based on the finite size of the particles. The velocity fields show the presence of elongated streamwise structures. The largest length scales are found in the transition region, where average integral length scales up to 5D are found. The structures decrease in length when the flow has fully transitioned to a turbulent state.

Onset of turbulence in particle-laden pipe flows

“…Here μ 0 is the viscosity of the continuous phase (i.e., saline water or glycerol). In a previous study, the integral length scales corresponding to a smooth transition case were found to be smaller (i.e., approximately 4D in the transition region) and continuously present [14]. This is in contrast to a sharp, intermittent transition, where turbulent patches span about 20D-30D [15,18].…”

“…Previously, it was shown that the velocity fluctuations caused by the finite-sized particles scale with d/D. Based on this, it is expected that Re s,c is dependent on d/D and φ [14]. The latter has been shown to be a relevant scaling parameter before [8][9][10] In both plots a selection of three representative cases is shown.…”

“…Hogendoorn et al [14] showed that for large d/D even very dilute systems (φ = 0.0025) exhibit this particle-induced transition. Based on instantaneous velocity measurements, they showed that particles introduce perturbations and formulated a model predicting that these disturbances are proportional to d/D and U .…”

“…All four particle types are used in the 10.00 mm facility, and the 1.31 and 1.75 mm particles are also used in the 19.98 mm facility. This results in six d/D ratios (0.03, 0.053, 0.065, 0.088, 0.13, and 0.18); two pressure data sets were reused from previous studies (d/D = 0.18, 0.053 [9,14]).…”

“…In the literature, generally, three different regimes are distinguished to describe the underlying dynamics: classical, intermediate, and particle-induced transition behaviors [9,10,14]. Using the perturbation amplitude [Eq.…”